This paper presents new, computationally efficient algorithms for solution and estimation of nonlinear dynamic rational expectations models. The innovations in the algorithms are as follows: (1) The entire solution path is obtained simultaneously by taking a small number of Newton steps, using analytic derivatives, over the entire path; (2) The terminal conditions for the solution path are derived from the uniqueness and stability conditions from the linearization of the model around the terminus of the solution path; (3) Unit roots are allowed in the model; (4) Very general models with expectational identities and singularities of the type handled by the King-Watson (1995a,b) linear algorithms are also allowed; and (5) Rank-deficient covariance matrices that arise owing to the presence of expectational identities are admissible. Reasonably complex models are solved in less than a second on a Sun Sparc20. This speed improvement makes derivative-based estimation methods feasible. Algorithms for maximum likelihood estimation and sample estimation problems are presented.